Friday, March 25, 2016

GPS Always Overestimates Distances

Researchers in Austria and the Netherlands have pointed out that existing GPS applications almost always overestimate the distance of a trip, no matter where you're going. Why? Granted some small amount of random error in measuring each of the waypoints along a trip, the distance between erroneous points on a surface is overwhelmingly more likely to be greater than, rather than lesser than, the true distance -- -- and over many legs of a given trip, this error adds up to a rather notable overestimate. And to date no GPS application makers have corrected for it. A wonderful and fairly simple piece of math, one that was lurking under our noses for some time that no one thought to check, that should improve all of our navigation devices:

2 comments:

Maybe it doesn't need to be corrected. As a consumer of GPS, I'd rather have a systematic bias to long estimates than short estimates, just as I'd rather have an alarm clock that runs fast over one that runs slow, or even one that keeps perfect time. As the folks in career counseling say, to be just on time is to be late.

Assuming you do want to correct for the bias, is there a particular method you have in mind? I question whether it's even a well-defined problem. Measuring the trajectory of a person in transit is like measuring a coastline in that a higher sampling rate can sometimes reveal a much longer arc length. If I'm taking a walk with a cell phone in my pocket, the phone's elevation will have its ups and downs, and its (mostly) forward progress will have periodic accelerations and decelerations. Seems like that could be a frightfully long arc length. In-car GPS has the option of comparing a priori distance estimates to odometer readings, so a fudge factor obtained by that method would at least be empirical in origin. But does the odometer not also have a bias in the direction of overstating distance? It would seem that when you're spinning your wheels trying to get unstuck from snow or something your odometer is making more progress than you are. Maybe that gets offset by those times you see the yellow sign that says "BUMP" and you step on it...

Well, that's a pretty good observation. The linked article asserts that the steps on a GPS-mapped path are pretty small (1m or 5m). And, at the end, that runners and other athletes have complained for some time that the GPS is noticeably overestimating their performance (i.e., it's a real problem that the reported distances are greater than the actual distance run).

Not being an expert in the particular issue, but I would think that you'd want a solution in the GPS software itself, not tied to a particular vehicle's odometer (e.g., it wouldn't fix the problem experienced by runners). If the overestimate is between 12% and 20% of actual distance, then my instinct was that you could just scale it by a proportion (like down by about 16% or so). Maybe that proportion is dependent on length of the steps involved (1m, 5m, or something else).